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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 521643, 10 pages
http://dx.doi.org/10.1155/2014/521643
Research Article

On the Minimal Polynomials and the Inverses of Multilevel Scaled Factor Circulant Matrices

Department of Mathematics, Linyi University, Linyi, Shandong 276000, China

Received 27 April 2014; Revised 21 May 2014; Accepted 21 May 2014; Published 5 June 2014

Academic Editor: Tongxing Li

Copyright © 2014 Zhaolin Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Circulant matrices have important applications in solving various differential equations. The level-k scaled factor circulant matrix over any field is introduced. Algorithms for finding the minimal polynomial of this kind of matrices over any field are presented by means of the algorithm for the Gröbner basis of the ideal in the polynomial ring. And two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for computing the inverse of partitioned matrix with level-k scaled factor circulant matrix blocks over any field is given by using the Schur complement, which can be realized by CoCoA 4.0, an algebraic system, over the field of rational numbers or the field of residue classes of modulo prime number.